Fiber lasers and amplifiers make use of a dielectric waveguide, the fiber, to constrain the degrees of freedom of the electromagnetic field while it is amplified by excited laser atoms within the core of the fiber. Given an amplifying waveguide, a fiber laser is formed by introducing it into a resonant cavity. One of the main advantages of fiber lasers is that if a single transverse waveguide mode is present in the fiber, then the output will have diffraction limited beam quality. Only one type of dielectric waveguide is considered here, a modified total internal reflection photonic crystal fiber (MTIR PCF), also known as solid-core photonic crystal fiber, microstructured fiber, or holey fiber. All fibers are assumed to be uniform along their length (axisymmetric) and, therefore, completely determined by the geometry of their cross-section.
FIG. 1 is a typical MTIR PCF with plots showing relevant parameters. FIG. 1a is the cross-section of a standard photonic crystal fiber lattice with 10-micron spacing between lattice elements. It consists of an array of air-filled circular inclusions 12 in the fiber material 11 and a core 13 comprised of an area in the fiber material 11 in the center that is missing air holes. The inner cladding 11 is enclosed by an outer cladding 14. The multimode central core 13 is appropriately doped with an active lasing ionic species designed for operation at a desired fundamental wavelength mode. The array can be described as a uniformly spaced lattice with one or more defects comprising the core and consisting of a missing or filled-in hole. FIG. 1b is a plot of the calculated effective index vs. mode number of the lattice in FIG. 1a. The plot in FIG. 1c shows the calculated fundamental (solid line) and higher order (dashed lines) core normalized modal intensity vs. the position within the core in units of lattice spacing (10 microns). The arrows between FIGS. 1b and 1c show the effective index correspondence of the modes.
The guiding mechanism for a MTIR PCF can be thought of in the context of total internal reflection. Rays within the core that hit the air holes will be reflected due to the index difference on the boundary of the air hole. Maxwell's equations may be solved to determine the detailed characteristics of the guided mode.
In general, the modes of an MTIR-PCF may be described by an electromagnetic field distribution over the cross-section of the fiber and a propagation constant that determines the periodicity of the fields along the axis of the fiber at a given optical wavelength. In addition to the guided modes, there are also modes that are not localized to the core. In these modes, the field intensity is spread across the cladding and they are called cladding modes. Their properties will be determined by the geometry of the cladding, specifically, the index difference at the cladding boundary. Double-clad fibers have a region outside the cladding in order to confine pump light to the cladding. These fibers are also called cladding pumped fibers. Single-clad fibers have no special material outside the cladding except that which provides mechanical stability to the fiber.
The signal in the core of a single-mode fiber also experiences loss as a result of manufacturing irregularities and physical perturbations such as bending. The lost energy transfers to the cladding modes in this case. This can be viewed as a coupling process. The irregularities cause the core mode to couple to the cladding modes. Cladding modes may also be characterized by a field distribution and propagation constant.
The maximum power in a diffraction-limited beam from rare-earth doped fiber lasers is limited by the maximum electromagnetic intensity that can persist within the core without undesired effects and the maximum core area that can operate with a single propagating transverse mode. The intensity limit is fixed by the material properties. Therefore, any significant increase in power output must be achieved by increasing the core size and flattening the mode for a given maximum intensity level. As the core size of a modified total internal reflection photonic crystal fiber is increased, either the beam quality degrades due to the propagation of multiple transverse modes, or the fundamental mode losses become excessive as the waveguide is made weaker by decreasing the air hole size in order to eliminate the higher order modes. Standard single-mode fibers designed to operate at a wavelength of about 1 micron have a core diameter of approximately 7 microns. One successful strategy that has yielded a three-fold increase in core size is to use a fiber with a core supporting multiple modes, but then introducing mode-dependent losses so that the higher order modes experience more loss than the fundamental mode. In other words, the higher order modes experience a greater amount of coupling into the cladding modes. By the time the signal reaches the output of the fiber, only the fundamental mode is propagating in the fiber core.
In practice this mode discrimination is often accomplished in a step index fiber by coiling the fiber at an optimal radius. A coiled fiber exhibits substantially more loss in the higher order modes than the fundamental for a core sized up to approximately 25 microns (Koplow et. al., Optics Letters, 25, 442 (2000).) Above this diameter, however, the loss differential between the modes becomes so small that it does not sufficiently discriminate the fundamental mode from the higher order modes during amplification. (Liu et. al., SSDLTR 2004 paper, FIBER-5 (2004).) If larger area cores are sought, the tradeoff between fundamental mode loss and multi-mode operation is unavoidable if the cladding around the core is uniform, either in the sense of having a uniform index of refraction or having a uniform array of air holes in the case of the MTIR PCF. The uniformity of the cladding causes the cladding modes to couple uniformly to the fundamental mode and the undesired higher order guided modes leading to inefficient mode discrimination.
The maximum power in a diffraction-limited beam from rare-earth doped fiber lasers is currently limited by the maximum core area that can operate with a single propagating transverse mode and the maximum intensity permitted by material limitations. Increases in the core area is the subject of co-pending U.S. patent application Ser. No. 11/204,146 filed Aug. 15, 2005 and is hereby incorporated by reference. That application enabled large increases in the core area but with a relatively narrow profile of the fundamental mode intensity curve.
Further power increases will not only require a fiber with a larger core area as obtained with the tuned cladding fiber designed for a multimode central core, but also will need to flatten the intensity curve for a given maximum intensity level.